MPs are to question the UK Border Agency (UKBA) and a private security firm about the death of a man who collapsed while being deported from Britain last week.

Keith Vaz, the chairman of the Commons home affairs select committee, told the Guardian Lin Homer, the UKBA chief executive, had agreed to answer questions on Jimmy Mubenga's death and the wider issue of the use of restraint during immigration deportations.

The private security company G4S, three of whose escort officers have been arrested over the deportation, has also agreed to answer MPs' questions.

Vaz said he had also written to the British Airports Authority asking if it had any more evidence, particularly closed-circuit television footage.

The UKBA chief will take part in a home affairs select committee evidence session on wider immigration issues, already scheduled for a fortnight's time.

The Metropolitan police said on Monday it had interviewed "by appointment" at a west London police station the three G4S officers, and they had been released on police bail until a date in December. The Met's homicide and murder unit is investigating the death, which the police say is unexplained at this stage.

Mubenga, 46, died after losing consciousness on BA flight 77 on Tuesday last week. Four passengers have since told the Guardian they saw the three escort officers heavily restraining Mubenga, who consistently complained about his breathing.

According to the witnesses, Mubenga was handcuffed and sitting between two guards at the rear of the aircraft. They kept him restrained in his seat as he began shouting and seeking to resist deportation.

Police and paramedics were called when Mubenga lost consciousness, and the aircraft, which had been due to take off, returned to the terminal.

Vaz wrote to the home secretary, Theresa May, about the case over the weekend, saying: "If, as eyewitness reports suggest, Mr Mubenga was complaining of breathing difficulties, questions must be asked as to why help was not called for sooner. When removing people from the UK, human rights must be fully respected at all times."